Question 128
The magician Magimático asks a person in the audience to choose any piece of a standard domino set. Such a piece is formed by a pair of numbers from 0 to 6. Then he asks the person to choose one of the numbers on the piece and to perform the following sequence of operations:
1. multiply it by 5;
2. add 15 to the previous result;
3. multiply the last result by $2$ and, finally,
4. add the other number of the piece to the last result.
After these operations are carried out, the result is announced and Magimático impresses the audience by saying exactly the numbers written on the chosen domino.
a) Knowing that the result was 62, how did the magician discover the number chosen by the audience member?
b) If the result had been $n$, how can one find the numbers of the chosen piece?
1. multiply it by 5;
2. add 15 to the previous result;
3. multiply the last result by $2$ and, finally,
4. add the other number of the piece to the last result.
After these operations are carried out, the result is announced and Magimático impresses the audience by saying exactly the numbers written on the chosen domino.
a) Knowing that the result was 62, how did the magician discover the number chosen by the audience member?
b) If the result had been $n$, how can one find the numbers of the chosen piece?